Generic, reduced state, maximum likelihood decoder

ABSTRACT

A decoder includes at least one programming input for a plurality of programmable reduced-state trellis parameters. A programmable device is connected to the at least one programming input and implements a reduced-state maximum likelihood decoder that is operable for processing a continuous phase modulated (CPM) signal and returning up to N bits that were transmitted based on a maximum likelihood and current winning super-state and corresponding survivor full-state. The programmable device calculates the path metrics for every super-state and determines a best path based on the reduced-state trellis parameters.

FIELD OF THE INVENTION

The present invention relates to communication systems, and moreparticularly, this invention relates to maximum likelihood decoding usedin communication systems.

BACKGROUND OF THE INVENTION

An error correction and detection system used in communication systemsdetects errors due to noise or other signal impairments duringtransmission to enable error localization and error correction. Forwarderror correction (FEC) permits error control for data transmission, anddiffers from standard error detection and correction systems because thereceiver can correct errors without requesting a retransmission of data.The design of the code used in any FEC system determines the maximumfraction of errors that can be corrected in advance. As a result,different FEC codes can be suitable for different conditions.

For example, in many FEC schemes, redundancy is added to transmitteddata using a predetermined algorithm. Each of the redundant bits is acomplex function of the original information bits. As a result, theencoded output may or may not include the original information.Unmodified inputs at the output are systematic codes and those that arenot are non-systematic.

FEC schemes could be considered to average the noise because each databit affects many transmitted symbols. Some symbols are corrupted more bynoise than others and this allows the original data to be extracted fromthe other, less corrupted received signals that depend on the same userdata. As FEC codes approach the theoretical Shannon limit and strongercodes are used, an FEC scheme works well above a minimum signal-to-noiseratio, but typically fails when the signal is below that minimum ratio.

For higher modem data rates, for example, greater than 1 Mbps, thecomputational complexity of FEC schemes can be prohibitive given thecurrent state of commercially available digital signal processors (DSPs)and Field Programmable Gate Array (FPGA) technology.

The use of Forward Error Correction (FEC) and the Maximum LikelihoodDecoder (e.g. Viterbi Algorithm) are described exhaustively in moststandard communications texts including “Digital Communications” by JohnG. Proakis. Continuous Phase Modulation is described in detail in bookssuch as “Digital Phase Modulation” by Anderson, Aulin and Sundberg and“Digital Communications” by John G. Proakis.

In digital communications systems, for example, cellular and PCS(personal communications systems), computer communications systems, andSATCOM (satellite communications) systems, digital data is modulated bythe modem onto a signal to be transmitted over a communications channel.Data is typically encoded before transmission to a receiver or to astorage device, to protect the data from errors, which may result from anoisy communications channel or a defect in the storage medium. Anencoder manipulates data symbols in accordance with an error correctioncode and produces error correction symbols or a structured redundancyoutput sequence. When the code word is later received or retrieved it isdecoded to reproduce the data symbols, and errors in the data symbolsare corrected, if possible, using the error correction symbols or thestructured redundancy of code.

For the following discussion, a convolutional codeword is defined as then output bits that are generated based on an input of k input bits(i.e., rate k/n code). One method of decoding code words encoded using aconvolutional code is maximum likelihood decoding. One kind of maximumlikelihood decoder is commonly referred to as a Viterbi decoder.Conceptually, a Viterbi decoder uses a decoding trellis, which has abranch for each possible code word and connected paths of branches foreach possible stream, or sequence, of code words. The decoderessentially finds a path through the trellis, which is “closest” to, ormost like, the received stream of code words. It then treats the codewords on this “most likely” trellis path as the received code words andassigns data values to them, to produce a best estimate of thetransmitted data.

To determine the most likely path, the decoder calculates, for eachreceived code word, a set of branch metrics as numerical representationof the likelihood that the transmitted code word, which may containerrors on reception, is actually the code word which corresponds to aparticular branch. In one such decoder the branch metrics are theHamming distances between the received code word and the code wordsassociated with the various branches.

Each branch in the decoding trellis leads from an initial state, whichrepresents the state that the registers are in prior to the formulationof the code word associated with the branch, and leads to an end state,which represents the state that the registers are in after theformulation of the code word. For a binary code there are 2^(K−1)possible states associated with each decoding level, where K is theconstraint length of the code. For example, the code may have aconstraint length of 3, i.e., there are 2 registers, and there are thus4 possible register states, namely, 00, 01, 10, 11, in each decodinglevel. Since the code is a rate 1/n code, i.e. binary code so k=1, thereare two possible branches leading from each initial state, namely abranch associated with a zero data bit and a branch associated with aone data bit. Each of these branches necessarily leads to a differentend state. Thus, for each of the 2^(K−1) states in a given decodingstage, there are two branches leading to each of these states, and eachbranch may represent the transmitted code word. Accordingly, to decodethe code word the decoder must determine two branch metrics for each ofthe 2^(K−1) possible end states, or a total of 2(2^(K−1)) branchmetrics. For convolutional codes, there are only 2^(n) unique branchmetric values.

Once the decoder calculates these branch metrics, it next determines themetrics of the various paths leading to the end states. Accordingly, thedecoder adds to the branch metrics the appropriate path metrics, whichare the sums of the branches leading to the current starting states. Thedecoder then selects a most likely path leading to each of the endstates and stores for later use the path metrics and information, whichidentifies these most likely paths. These most likely paths, which arealso referred to as the “surviving paths.” The decoder does not retaininformation relating to the less likely, or non-surviving, paths. Inthis way, the decoder “prunes” these paths from the trellis, and therebyeliminates for a next level of decoding a portion of the path metriccalculations.

When a sufficient number of code words have been included in the trellispaths, the most likely code word path is chosen from the surviving pathsassociated with the end states. The decoder selects as the most likelypath the code word path which is “closest” to the received data, i.e.,the path with the smallest Hamming distance metric. The decoder thendecodes the code words on the most likely path, or “traces back” alongthe path, to determine the associated data bits.

The Viterbi algorithm is used not only to decode convolutional codes butalso to produce the maximum-likelihood estimate of the transmittedsequence through a channel with intersymbol interference (ISI), and todecode trellis-coded modulation (TCM) and other modulations with memory.The Viterbi decoder is typically divided into three functional parts.The first part is an add-compare-select (ACS) unit that is used tocalculate the path metrics. The second part is the survivor memorycontrol unit for survivor memory management, which may store thesurvivor sequences as last part of the Viterbi decoder.

Continuous phase modulation (CPM) is being applied in communications dueto its bandwidth efficiency and constant envelope characteristics. WithCPM, the modulated signal phase transitions are smoothed. For example,with Binary Phase-Shift Keying (BPSK), a logic one is transmitted as onephase of a modulated signal, and a logic zero is transmitted as180-degree phase-shifted with a sharp transition (i.e., instantaneous)in phase. This sharp phase transition results in broadening of thetransmitted spectrum. With CPM the phase of the transmitted signal makessmooth phase changes over the bits of the modulating digital signal. Anexample of CPM is Minimum Shift Keying (MSK) modulation.

Multi-h continuous phase modulation (multi-h CPM) is itself a broadclass of modulated waveforms. The class includes signals with constantamplitude but varying phase. Multi-h CPM differs from the single-hformat by using a set of H modulation indices in a cyclic manner. Thisresults in the delayed merging of neighboring phase trellis paths andultimately, in improved error performance. A detailed description ofmulti-h CPM waveforms is included in the book “Digital Phase Modulation”by Anderson, Aulin, and Sundberg, Plenum Press, New York, 1986.

As described by articles in Svensson, “Reduced State Sequence Detectionof Full Response Continuous Phase Modulation,” Electronics Letter, May10, 1990, Vol. 26, No. 10; and Eyuboglu et al., “Reduced State SequenceEstimation With Set Partitioning and Decision Feedback,” IEEETransactions on Communications, January 1988, Vol. 36, No. 1, (andothers), some techniques reduce the complexity of the standard MLSE(Maximum Likelihood Sequence Estimator) decoders. For example, inEyuboglu, a reduced-state sequence estimator for linear intersymbolinterference (ISI) channels uses a conventional Viterbi algorithm (VI)with decision feedback to search in a reduced-state “subset trellis”which is constructed using set partitioning principles. The complexityof maximum likelihood sequence estimation (MLSE) due to the length ofthe channel memory and the size of the signal set is systematicallyreduced. An error probability analysis shows that a goodperformance/complexity tradeoff can be obtained. In Svensson, a reducedstate sequence detector (RSSD) combines decision feedback with Viterbidecoding for M-ary full response continuous phase modulation. Thedetector is analyzed with minimum Euclidean distances and by simulationsof the symbol error probability. The M-ary full response CPM schemes canbe decoded by a decoder with only two states, when the modulation indexis relatively small (<1/M) and for larger modulation indexes less thanone with M states. There are several variants of the reduced state MLSEdecoders, which do not provide the same (reduced) complexity or modembit error rate performance.

The use of Forward Error Correction (FEC) and the maximum likelihooddecoder (Viterbi algorithm) is described in most standard communicationstexts. Reduced state sequence estimation (RSSE) was an importantdevelopment in MLSE decoder design in the 1980's. The developers andmanufacturers XILINX and Altera produce FPGA and VHSIC HardwareDescription Language (VHDL) tools that allow users a few programmableViterbi (NLSE) options. These are usually formed as convolutional codeswith the ability to provide soft decision metrics. None of the currenttools provide for a desired decision feedback or trellis structuremanipulation required for reduced-state sequence estimation. They alsoare not programmable for use with CPM signals and signals with memory.Also, there exists a need in the industry for a reduced state, generic,programmable maximum likelihood decoder.

SUMMARY OF THE INVENTION

A decoder includes at least one programming input for a plurality ofprogrammable reduced-state trellis parameters. A programmable device isconnected to the at least one programming input and implements areduced-state maximum likelihood decoder that is operable for processinga continuous phase modulated (CPM) signal and returning up to N bitsthat were transmitted based on a maximum likelihood and current winningsuper-state and corresponding survivor full-state. The programmabledevice calculates the path metrics for every super-state and determinesa best path based on the reduced-state trellis parameters.

The programmable reduced-state trellis parameters are formed from one ofat least a number of super-states, the number of full-states, the numberof branches per super-state, a reverse super-state trellis table, adecoder super-state survivor as a full-state, a forward full-statetable, a full-state to super-state mapping table, decoder super-statepath metric and decoder super-state traceback array. All programmableparameters are integers. The decoder state structure can be formed of apath metric per super-state, a traceback array per super-state, and asurvivor full-state per super-state. The reduced-state trellis structurecan be formed from an Ungerboeck-style set-partitioning algorithm. Areduced-state trellis structure can be formed from a two-stateSvensson-style structure or an M-state Svensson-style structure.

The decoder state structure could contain path metrics and a fulldecoder state used for decision feedback. The reduced-state maximumlikelihood decoder could be formed as a forward trellis structureoperative for indicating which full decoder state from a decisionfeedback is connected to a full decoder state for any given symbol. Atleast one output can be connected to the programmable device foroutputting decoded bits with multiple bits per output. An output can beoperative for outputting a full traceback of decoded bits for a bestpath.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention willbecome apparent from the detailed description of the invention whichfollows, when considered in light of the accompanying drawings in which:

FIG. 1 is a high-level diagram of a reduced state trellis structure, inaccordance with one non-limiting example of the present invention.

FIG. 2 is a high-level diagram of a two-state, reduced-state trellisstructure, in accordance with one non-limiting example of the presentinvention.

FIG. 3 is a block diagram of an example of a communications system thatincludes various radios, which could include decoders in accordance withthe present invention.

FIG. 4 is a block diagram of a receiver that includes a programmabletrellis decoder that can be modified for use in accordance with thepresent invention as a reduced-state, generic and programmable maximumlikelihood decoder as a trellis decoder.

FIG. 5 is a more detailed block diagram of the reduced-state, genericand programmable trellis decoder shown if FIG. 4.

FIG. 6 is a flow chart illustrating steps in a method of implementing areduced-state, generic and programmable trellis decoder, in accordancewith a non-limiting example of the present invention.

FIG. 7 is a graph showing phase pulse shapes for 16 samples per symbol.

FIG. 8 is a block diagram showing a full-state trellis structure witheight states for in h=¼ binary CPFSK.

FIG. 9 is a block diagram showing a h=¼ CPFSK constellation.

FIG. 10 is a graph showing a BER comparison of MIL-STD-188-181C, H=(4/16, 5/16) 4-ary CPFSK set-partitioning reduced-state model.

FIG. 11 is a diagram showing a four-state trellis structure.

FIG. 12 is a graph showing the BER comparison of MIL-STD-188-181C, H-(4/16, 5/16) 4-ary CPFSK with tilted phase reduced-state model.

FIG. 13 is a graph showing a hybrid AM pulse spectra.

FIG. 14 is a graph showing a hybrid phase pulse spectra.

FIG. 15 is a graph showing an AM pulse shape performance.

FIG. 16 is a graph showing a PM pulse shape performance.

FIG. 17 is a graph showing a reduced state h=⅓ amplitude shaped HCPM biterror rate, in accordance with a non-limiting example of the presentinvention.

FIG. 18 is a graph showing a reduced state h=⅓ phase shaped HCPM biterror rate, in accordance with a non-limiting example of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Different embodiments will now be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsare shown. Many different forms can be set forth and describedembodiments should not be construed as limited to the embodiments setforth herein. Rather, these embodiments are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope to those skilled in the art. Like numbers refer to like elementsthroughout.

The system and method, in accordance with a non-limiting example of thepresent invention, provides a reduced-state sequence estimation (RSSE)generic and programmable decoder that has input programmability for thenumber of super states in each trellis. Full states can be combined toform super states. There are a number of branches per super state and anumber of trellis structures. The plurality of programmable super statetrellis parameters preferably includes trellis connectivity informationfor trellis stages, active and inactive super state for each trellisstage, a trellis branch transition data value and a metric index fortrellis branch transition, and may include a number of trellisstructures, a number of trellis super states for each trellis structure,and a number of branches for each trellis super state. The reverse statetrellis structure connects each super state with a list of previoussuper states. The decoder super state structure contains path metricsand a “winning” full state used for decision feedback. A forward statetrellis can define which full state from the decision feedback isconnected to the next full state for any given bit. The output of thedecoder includes decoded bits with multiple bits per output and a fulltraceback of all decoded bits for that path. The difference between thebest and worst path metrics can be provided and the “winning” state forthe current best path chosen. Also, the trellis structure may include areverse-state trellis structure and/or a forward-state trellisstructure.

Some existing communications devices have limited program space, CPUcomputation speed and battery power. To meet these requirements, asoftware-based or FPGA-based reduced state maximum likelihood decoder inaccordance with non-limiting examples of the present invention supportsdemodulation of waveforms with memory. It is also programmable andsupports demodulation of Continuous Phase Modulation (CPM) and decodingof most FEC trellis codes. The reduced state decoder in accordance withnon-limiting examples of the present invention varies from most standardtrellis decoders because of non-limiting features that include:

1) The decoder state table has a “winning full states memory, inaddition to maintaining the winning” path metric; and

2) The decoder has a forward trellis structure (linked list) thatindicates how each full state in the decoder is connected to the nextfull state.

Although reduced state decoders are described in many publications, thedecoder in accordance with a non-limiting example includes a“one-size-fits-all” approach for the design of the decoder state tableand the trellis structure. A single implemented FPGA/DSP (digital signalprocessor) architecture can decode most trellis codes or memory based(i.e., CPM) modulation schemes.

The reduced-state Viterbi detector has a reduced complexity of hardwareand uses a reduced-state trellis. The detector could consider ashortened impulse response and cancel intersymbol interference due tothe tail of the impulse response for each state by using past survivorsymbols, in some non-limiting examples. In an RSSE algorithm, the numberof states could be reduced by partitioning each element in a statevector into a given number of subsets and representing the subset vectoras a reduced state trellis. The reduced state could be done on the basisof Ungerboeck's set partitioning principles such that the impulseresponse data are estimated according to the maximum likelihood sequenceestimation (MLSE) method via the Viterbi algorithm. A transmit sequencecan be estimated from possible data sequences taking into account thereceived sequence and estimated impulse response of a transmissionsystem. RSSE can reduce the complexity of the MLSE by truncating channelmemory or applying set partitioning to the signal alphabet. RSSEalgorithms can search for the most likely data sequence in the reducedtrellis by keeping only the best survivor or winning paths for eachreduced state. Several states can be merged, and thus, reduce thecomplexity of the MLSE. Each super state in a reduced-state trellis canbe formed by combining states of the original maximum likelihood trellisusing the Ungerboeck-like set partitioning principles. When a binarytransmission is used, the RSSE algorithm could become a state-truncationtechnique, where each super state in the reduced-state trellis is formedby truncating the maximum likelihood state vector to a suitable length.

As noted above, an Ungerboeck style (set partitioning) reduced statetrellis structure for a h=¼ (8 states) Continuous Phase Frequency ShiftKeying (CPPSK) modulation is shown in FIG. 1. The full state labels aremarked in brackets and new super state labels listed above eachbracketed pair. This reduced state trellis structure is one-half ascomplex as the original trellis structure without any reduction in BitError Rate (BER) performance.

A Svensson style (2 state) approach for binary h=¼ CPFSK modulation isshown in FIG. 2. It has a similar trellis structure used for any(h-value) CPFSK modulation and reduces the trellis complexity by afactor of four (for h=¼). The maximum-likelihood sequence estimator asdefined in the incorporated by reference Svensson reference has only twostates (for binary full response CPM) and its trellis structure is shownin FIG. 2.

As illustrated, a one-valued bit causes a state transition and azero-valued bit does not. This can be implemented with little difficultyand can be adapted to any single-h binary CPFSK modulation. As with theset-partitioning approach, decision feedback is used to maintain thewinning phase state of each of the two super states. The decodercalculates the path metrics for the two valid paths from the chosen,winning phase and picks a new winning path metric, which is then savedin the super state based on the branch taken during the symbol. If thebranch corresponds to a 0-valued bit, then the new super state is thesame as the old super state. If, however, the transition corresponds toa one-valued bit, then the path metric transitions to the other superstate.

Referring now to FIGS. 3-6, an example of a communications system thatcan include various radios having the decoder used with the presentinvention is now set forth with respect to FIG. 3, followed by ahigh-level description of a reduced-state, generic and programmabletrellis decoder (FIGS. 4 and 5) and flowchart (FIG. 6) explaining thedecoder.

An example of a radio that could be used with such system and method inaccordance with non-limiting examples of the present invention is aFalcon™ III radio manufactured and sold by Harris Corporation ofMelbourne, Fla. It should be understood that different radios can beused, including software defined radios that can be typicallyimplemented with relatively standard processor and hardware componentsand mesh network radios. One particular class of software radio is theJoint Tactical Radio (JTR), which includes relatively standard radio andprocessing hardware along with any appropriate waveform software modulesto implement the communication waveforms a radio will use. JTR radiosalso use operating system software that conforms with the softwarecommunications architecture (SCA) specification (seewww.jtrs.saalt.mil), which is hereby incorporated by reference in itsentirety. The SCA is an open architecture framework that specifies howhardware and software components are to interoperate so that differentmanufacturers and developers can readily integrate the respectivecomponents into a single device.

The Joint Tactical Radio System (JTRS) Software Component Architecture(SCA) defines a set of interfaces and protocols, often based on theCommon Object Request Broker Architecture (CORBA), for implementing aSoftware Defined Radio (SDR). In part, JTRS and its SCA are used with afamily of software re-programmable radios. As such, the SCA is aspecific set of rules, methods, and design criteria for implementingsoftware re-programmable digital radios.

The JTRS SCA specification is published by the JTRS Joint Program Office(JPO). The JTRS SCA has been structured to provide for portability ofapplications software between different JTRS SCA implementations,leverage commercial standards to reduce development cost, reducedevelopment time of new waveforms through the ability to reuse designmodules, and build on evolving commercial frameworks and architectures.

The JTRS SCA is not a system specification, as it is intended to beimplementation independent, but a set of rules that constrain the designof systems to achieve desired JTRS objectives. The software framework ofthe JTRS SCA defines the Operating Environment (OE) and specifies theservices and interfaces that applications use from that environment. TheSCA OE comprises a Core Framework (CF), a CORBA middleware, and anOperating System (OS) based on the Portable Operating System Interface(POSIX) with associated board support packages. The JTRS SCA alsoprovides a building block structure (defined in the API Supplement) fordefining application programming interfaces (APIs) between applicationsoftware components.

The JTRS SCA Core Framework (CF) is an architectural concept definingthe essential, “core” set of open software Interfaces and Profiles thatprovide for the deployment, management, interconnection, andintercommunication of software application components in embeddeddistributed-computing communication systems. Interfaces may be definedin the JTRS SCA Specification. However, developers may implement some ofthem, some may be implemented by non-core applications (i.e., waveforms,etc.), and some may be implemented by hardware device providers.

For purposes of description only, a brief description of an example of acommunications system that would benefit from the present invention isdescribed relative to a non-limiting example shown in FIG. 3. Thishigh-level block diagram of a communications system 50 includes a basestation segment 52 and wireless message terminals that could be modifiedfor use with the present invention. The base station segment 52 includesa VHF radio 60 and HF radio 62 that communicate and transmit voice ordata over a wireless link to a VHF net 64 or HF net 66, each whichinclude a number of respective VHF radios 68 and HF radios 70, andpersonal computer workstations 72 connected to the radios 68,70. Ad-hoccommunication networks 73 are interoperative with the various componentsas illustrated. Thus, it should be understood that the HF or VHFnetworks include HF and VHF net segments that are infrastructure-lessand operative as the ad-hoc communications network. Although UHF radiosand net segments are not illustrated, these could be included.

The HF radio can include a demodulator circuit 62 a and appropriateconvolutional encoder circuit 62 b, block interleaver 62 c, datarandomizer circuit 62 d, data and framing circuit 62 e, modulationcircuit 62 f, matched filter circuit 62 g, block or symbol equalizercircuit 62 h with an appropriate clamping device, deinterleaver anddecoder circuit 62 i modem 62 j, and power adaptation circuit 62 k asnon-limiting examples. A vocoder circuit 62 l can incorporate the decodeand encode functions and a conversion unit which could be a combinationof the various circuits as described or a separate circuit. These andother circuits operate to perform any functions necessary for thepresent invention, as well as other functions suggested by those skilledin the art. Other illustrated radios, including all VHF mobile radiosand transmitting and receiving stations can have similar functionalcircuits.

The base station segment 52 includes a landline connection to a publicswitched telephone network (PSTN) 80, which connects to a PABX 82. Asatellite interface 84, such as a satellite ground station, connects tothe PABX 82, which connects to processors forming wireless gateways 86a, 86 b. These interconnect to the VHF radio 60 or HF radio 62,respectively. The processors are connected through a local area networkto the PABX 82 and e-mail clients 90. The radios include appropriatesignal generators and modulators.

An Ethernet/TCP-IP local area network could operate as a “radio” mailserver. E-mail messages could be sent over radio links and local airnetworks using STANAG-5066 as second-generation protocols/waveforms, thedisclosure which is hereby incorporated by reference in its entiretyand, of course, preferably with the third-generation interoperabilitystandard: STANAG-4538, the disclosure which is hereby incorporated byreference in its entirety. An interoperability standard FED-STD-1052,the disclosure which is hereby incorporated by reference in itsentirety, could be used with legacy wireless devices. Examples ofequipment that can be used in the present invention include differentwireless gateway and radios manufactured by Harris Corporation ofMelbourne, Fla. This equipment could include RFS800, 5022, 7210, 5710,5285 and PRC 117 and 138 series equipment and devices as non-limitingexamples.

These systems can be operable with RF-5710A high-frequency (HF) modemsand with the NATO standard known as STANAG 4539, the disclosure which ishereby incorporated by reference in its entirety, which provides fortransmission of long distance HF radio circuits at rates up to 9,600bps. In addition to modem technology, those systems can use wirelessemail products that use a suite of data-link protocols designed andperfected for stressed tactical channels, such as the STANAG 4538 orSTANAG 5066, the disclosures which are hereby incorporated by referencein their entirety. It is also possible to use a fixed, non-adaptive datarate as high as 19,200 bps with a radio set to ISB mode and an HF modemset to a fixed data rate. It is possible to use code combiningtechniques and Automatic Repeat Request (ARQ).

There now follows a description of an example of a reduced-state,generic and programmable trellis decoder in accordance with non-limitingexamples of the present invention. Referring initially to FIGS. 4 and 5,an embodiment of a data communications receiver 110, such as a UHFsatellite communications receiver, including a reduced-state, genericprogrammable trellis decoder 130 will be described. Encoded andmodulated signals sent over a communications channel 112 are received bythe receiver 110. These modulated signals could be any signals withmemory such as CPM, ISI channels or trellis coded modulation (TCM). Ademodulator 120 processes the incoming signal, then sends the basebanddemodulated signal to the programmable trellis decoder 130. Theprogrammable trellis decoder 130 processes the signal and then sends thedecoded data and other related information to a destination over thechannel 114. The components of the receiver, e.g. the demodulator 120and the programmable trellis decoder 130, are controlled by a processor150.

The reduced-state, generic programmable trellis decoder 130 uses theRSSE algorithm and methodology explained above, and includes at leastone programming input 134, 136 for a plurality of programmable trellisparameters. It should be understood that the reduced-state decoder, inaccordance with a non-limiting example of the present invention, variesfrom a standard trellis decoder because the decoder state table has a“winning full state” memory in addition to maintaining the “winning”path metric. The decoder has a Forward Trellis structure as a linkedlist that indicates how each full state in the decoder is connected tothe next full state. Thus, a single implemented field programmable gatearray and digital signal processing architecture can decode any trelliscode, ISI channel or memory-based modulation, i.e., CPM.

The reduced-state sequence estimation programmable decoder can have aninput programmability that includes the number of super states in eachtrellis stage, number of trellis stages and which full states arecombined to form the super states. It can also include inputprogrammability for the number of branches per super state, the numberof trellis structures, a reverse-state trellis structure that connectseach super state with a list of previous super states, active andinactive states for each trellis stage, a trellis branch transition datavalue and a metric index for trellis branch transition. The decodersuper state structure can contain path metrics and a “winning” fullstate that is used for decision feedback. A forward-state trellis candefine which full state from the decision feedback (i.e., survivor path)is connected to the next full state for any given bit.

The output of the decoder could include decoded bits with multiple bitsper output. The full trace back of all decoded bits for that path can beincluded. The output can include the difference between the best andworst path metrics and the “winning” state for the current best path.

The decoder could include an add-compare-select (ACS) unit to receive asequence of trellis coded bits and calculate path metrics and outputsequences based upon branch metrics associated with each branch of atrellis-state diagram, a survivor memory for storing the outputsequences, and a survivor memory control unit to control the survivormemory and output decoded bits of the stored output sequences, as wouldbe appreciated by those skilled in the art.

A programmable device 132 is connected to the programming input andimplements a programmable trellis decoder (e.g., a continuous phasemodulation (CPM) decoder) having at least one trellis structure definedbased upon the plurality of programmable trellis parameters. Theprogrammable device 132 may comprise a field programmable gate array(FPGA), for example.

An FPGA is a semiconductor device containing programmable logiccomponents and programmable interconnects. The programmable logiccomponents can be programmed to duplicate the functionality of basiclogic gates (such as AND, OR, XOR, NOT) or more complex combinatorialfunctions such as decoders or simple math functions. In most FPGA's,these programmable logic components (or logic blocks) also includememory elements, which may be simple flip-flops or more complex blocksof memories.

A hierarchy of programmable interconnects allows the logic blocks of anFPGA to be interconnected as needed by the system designer, somewhatlike a one-chip programmable breadboard. These logic blocks andinterconnects can be programmed after the manufacturing process by thecustomer/designer (i.e., “field-programmable”) so that the FPGA canperform whatever logical function is needed.

FPGA's are generally slower than their application-specific integratedcircuit (ASIC) counterparts, cannot handle as complex a design, and drawmore power. However, they have several advantages such as a shorter timeto market, ability to reprogram in the field to fix bugs, and lowernon-recurring engineering costs. Another alternative is complexprogrammable logic devices (CPLD's).

To define the behavior of the FPGA the user may provide a hardwaredescription language (HDL) or a schematic design in some non-limitingexamples. Common HDL's are VHDL and Verilog. Then, using an electronicdesign automation tool, a technology-mapped netlist is generated. Thenetlist can then be fitted to the actual FPGA architecture using aprocess called place-and-route, usually performed by place-and-routesoftware. The user can validate the map, place and route results viatiming analysis, simulation, and other verification methodologies. Oncethe design and validation process is complete, the binary file generatedcan be used to reconfigure the FPGA device. Such a binary file may bestored and/or input to the programmable device 132 via the control inputblock 134.

As a non-limiting example, the programmable trellis decoder 130 mayimplement CPM and preferably multi-h CPM. With CPM the phase of thetransmitted signal makes smooth phase changes over the bits of themodulating digital signal. An example of CPM is minimum shift keying(MSK) modulation. Multi-h continuous phase modulation (multi-h CPM) isitself a broad class of modulated waveforms. The class includes signalswith constant amplitude but varying phase. Multi-h CPM differs from thesingle-h format by using a set of H modulation indices in a cyclicmanner. This results in delayed merging of neighboring phase trellispaths and ultimately, in improved error performance.

One or more outputs 138, 140, 142 of the programmable device 132 areprovided for outputting decoded bits with multiple bits per output andthe full traceback of all decoded bits for a best path, for outputting adifference between a best and worst path metric, and/or for outputting awinning state for a current best path.

The reduced-state generic programmable trellis decoder 130 provides theappropriate structure and flexibility in the decoder to handle all theabove-mentioned trellis schemes. The active and inactive states pertrellis stage can be done by having a delta increment between states oran active/inactive flag. Active/inactive provides flexibility as theremay be cases where there are no good delta increments between currentand next active state. A different starting state for each trellis stagemay be provided to avoid extra computations but active/inactive stateworks here too. Metrics to be used as branch metrics are provided byuser based on required trellis stage, node identification and branchconnection. Only metrics for active super states need to be computed. Adifferent set of branch connections are included for each trellis stagevia a reverse lookup table at the add/compare/select point.

An example for Node 0 (if trellis has 16 states there would be 16 statesfor each trellis stage). The repeat structure may be 4 trellis stageslong and for each stage there would be active and inactive stages andreverse lookup tables. This type of structure would be required for amulti-h CPM, but this same structure could be used for less complicatedtrellis schemes by simply changing the connectivity of the trellisreverse look-up table and the choice of active/inactive states. Thus,the approach leads to a generic trellis decoder, which can handle manymore trellis schemes than simple convolutional/TCM decoders availablecurrently.

As an example, a multi-h CPM waveform may be demodulated with thegeneric programmable trellis decoder 130. Multi-h implies a differentmodulation index h for each CPM symbol. For the case of 2h, there aretwo different values of h that change every other symbol. For example,binary CPM with h0= 4/16, h1= 5/16. Even number symbols use modulationindex h0, and odd number symbols use modulation index h1. For h0= 4/16,the trellis backward connectivity is as follows (data 0 negativefrequency (i.e., data=−1); data 1=positive frequency):

Format: State number: previous data = 0 previous data = 1 State 0: 4 28State 1: 5 29 State 2: 6 30 State 3: 7 31 State 4: 8 0 State 5: 9 1State 6: 10 2 State 7: 11 3 State 8: 12 4 State 9: 13 5 State 10: 14 6State 11: 15 7 State 12: 16 8 State 13: 17 9 State 14: 18 10 State 15:19 11 State 16: 20 12 State 17: 21 13 State 18: 22 14 State 19: 23 15State 20: 24 16 State 21: 25 17 State 22: 26 18 State 23: 27 19 State24: 28 20 State 25: 29 21 State 26: 30 22 State 27: 31 23 State 28: 0 24State 29: 1 25 State 30: 2 26 State 31: 3 27

For h1 = 5/16, the trellis backward connectivity is as follows: State 0:5 27 State 1: 6 28 State 2: 7 29 State 3: 8 30 State 4: 9 31 State 5: 100 State 6: 11 1 State 7: 12 2 State 8: 13 3 State 9: 14 4 State 10: 15 5State 11: 16 6 State 12: 17 7 State 13: 18 8 State 14: 19 9 State 15: 2010 State 16: 21 11 State 17: 22 12 State 18: 23 13 State 19: 24 14 State20: 25 15 State 21: 26 16 State 22: 27 17 State 23: 28 18 State 24: 2919 State 25: 30 20 State 26: 31 21 State 27: 0 22 State 28: 1 23 State29: 2 24 State 30: 3 25 State 31: 4 26

Analyzing the trellis structure for symbols (stages) 1, 2, . . . , 8:

Format: H# Start_State Delta_State Stage 1 H0 0 2 Stage 2 H1 1 2 Stage 3H0 1 2 Stage 4 H1 0 2 Stage 5 H0 0 2 Stage 6 H1 1 2 Stage 7 H0 1 2 Stage8 H1 0 2

To decode Stage 1, start at state 0 and increment states by two for nextstate (i.e. only even states are active). For Stage 2, only decode oddstates. For Stage 3, decode only odd states and for Stage 4 decode onlyeven states and then pattern repeats.

This is why the generic programmable trellis decoder 130 provides theability to have active states and inactive states (for most generalcase) or start state and delta state (as a alternative embodiment).Also, the backward trellis structure is needed to decode CPM properly.

So, the initialization process of the generic programmable trellisdecoder 130 prior to use in demodulating waveform will now besummarized. The trellis structure includes: Stage N; TrellisConnectivity; Active/Inactive States; Data Value causing Transition(i.e., branch transition data value); and Metric index for given trellisbranch transition.

First, the trellis structure (e.g., for CPM or other) is analyzed todetermine active/inactive states and connectivity. The connectivityinformation is written to decoder for as many trellis stages as isnecessary before pattern repeats (typically just one stage forconvolutional codes, two for 1 h CPM and four for 2h CPM example above).Active/inactive states (or start state and delta state) are written foreach trellis stage of trellis decoder (before pattern repeats). The datavalue that causes trellis branch transition is written to the trellisdecoder structure. The metric index used for trellis branch transitionis written to trellis decoder.

Example

Trellis Branch Structure Stage 0. The backward trellis structureincludes: State 0 from State 4 via a 0 bit using branch metric index 0;State 0 from State 12 via a 1 bit using branch metric index 1; State 1from State 5 via a 0 bit using branch metric index 2; State 1 from State13 via a 1 bit using branch metric index 3, etc.

To begin demodulating data: the branch metric array is written totrellis decoder (this will be used by decoder using the metric index;add/compare/select function is executed for each active state; tracebackfunction is executed to extract decoded information; and output data isprovided to user.

A method aspect of the invention is directed to a method of implementinga reduced-state generic programmable trellis decoder 130 (such as acontinuous phase modulation (CPM) decoder) and will be discussed withreference to the flowchart of FIG. 6. The method begins at block 200 andincludes, at block 202, providing a programmable device 132 (such as anFPGA) to implement the programmable trellis decoder 130 and includes atleast one trellis structure defined based upon a plurality ofprogrammable trellis parameters. The method further includes programmingthe plurality of programmable trellis parameters via at least oneprogramming input (block 204).

As discussed above, programming the plurality of programmable trellisparameters may include programming a number of trellis structures,programming a number of trellis states for each trellis structure, andprogramming a number of branches for each trellis state. The method mayinclude, at block 206, providing at least one output connected to theprogrammable device 132 for outputting decoded bits with multiple bitsper output and the full traceback of all decoded bits for a best path, adifference between a best and worst path metric, and/or a winning statefor a current best path.

To meet various requirements, an FPGA-based maximum likelihood decoderhas been designed which is reduced-state and programmable and willsupport demodulation of CPM, TCM and any FEC trellis code. It has beendesigned to support binary-h, 4-ary, CPM.

There follows now a description of reduced state decoder and theory ofoperation.

The Continuous Phase Modulation (CPM) waveform defined in theMIL-STD-188-181C Satellite Communications standard has a thirty-twostate trellis structure. The complexity of the maximum-likelihoodsequence estimator used to demodulate this signal is further increasedbecause the CPM signal has two modulation indices (h-values) thatrequire that the decoder store two sets of path metrics, one for each ofthe h-values. Approaches are taken to reduce the complexity of thetrellis structure of the CPM signal without significantly reducing thedemodulation performance for the range of signal to noise ratio valuesrequired by the UHF Satellite Communications standard. As noted before,the first state reduction method uses Ungerboeck-style set partitioning.Another approach utilizes a completely different 4-state trellisstructure with branch transitions defined that take advantage of thedifferential properties of the CPM modulation.

Continuous Phase Modulation is a constant envelope modulation with timedomain representation:

${s(t)} = {\sqrt{2{E/T}}\cos\;\left( {{2\pi\; f\; t} + {2\pi{\sum\limits_{i = 0}^{n}{\alpha_{i}h_{i}{q\left( {t - {iT}} \right)}}}}} \right)}$

where T is the symbol period, E is the energy per symbol, f is thecarrier frequency, α is the data symbol, h is the modulation index, andq is the phase pulse shape.

The UHF SATCOM standard provides for (up to) twelve different variationsof full-response, quaternary, multi-h CPM modulation schemes withdifferent symbol rates and modulation indices (h-values) to control thereceive complexity and transmit frequency spectra. All of the variantsresult in 32 phase states where only ½ of the states are active at anygiven symbol period. In all cases, there are two h-values defined as theratio p/q where q is always 16 and p alternates between even and oddinteger values.

There are two documented methods for reducing the number of states andthe corresponding receiver complexity. The first method, described byEyuboglu, combine states using the Euclidean distance as a metric(set-partitioning). The second method, described by Svensson, uses atilted-phase approach to CPM demodulation, which automaticallyeliminates the inactive states in the trellis. Svensson further reducesstates based on differential phase of each branch in the trellis.

As an illustration of the set-partitioning approach, the h=¼ binaryCPFSK (LREC CPM) trellis structure is drawn in FIG. 8.

The h=¼ CPFSK modulation has 8 full states. When the phase constellationis drawn with the phase positions labeled with each state (FIG. 9) itbecomes apparent that a trellis structure that creates super states bycombining full states 0 and 4, 1 and 5, 2 and 6, along with 3 and 7would provide the best distance for the reduced state trellis.

This CPM trellis structure already has two special properties. The firstis that, at each symbol, a valid starting state must either be odd oreven with the assumption that the first starting state is the zerostate. This is accomplished at the transmitter by starting thetransmission at a phase value of zero degrees. The second property ofthis full-state trellis is that the decoder can skip the calculation ofpath metrics for odd or even states at the decoding of every othersymbol. Thus, the optimal CPM decoder is already “reduced” to the pointthat it only calculates (updates) path metrics for half of the statesduring each decoder cycle.

Referring again to FIG. 1, the reduced-state trellis structure isillustrated. The full state labels are marked in brackets with the new,super state labels listed above each bracketed pair.

When constructing the reduced state trellis, each full state remainsconnected as it was in the original trellis. For this specific trellis,the characteristic properties of alternating the start state at eachsymbol decode cycle remains an important parameter of the decoder. Adecode cycle is defined as the calculation of a full state of branchmetrics from an input symbol and the update of the path metrics for allof the active states in the trellis structure.

Another enhancement required for reduced state sequence detection is thedecision feedback step in the decoder. Along with path metric andtraceback bits, the decoder should retain the winning full state at eachsuper state. Since it is assumed at the beginning that the decoderstarts at super state zero, the decoder state will also assume that thestarting full state is zero and not four. In general, the decoder superstate can be initialized to the first full state in the list for each ofthe reduced states (i.e. 0, 1, 2, and 3) by initializing the path metricproperly.

When the decoder calculates the path metric for super state one, it willcompare the zero to one transition (using the corresponding, calculatedbranch metric) to the metric for a state two to state one transition.The decoder will then save the full state value of one as the winningstate for the next decoder cycle (in other words, it retains the phaseof the survivor path). The next super state calculated at this decodercycle will be seven (skipping the even, invalid super states). Again,since zero is the winning full state from the initial decoder cycle, thetransition from zero to seven (the only valid full state) to the two tothree transition (since two was initialized in the previous decodercycle). The best path metric is chosen and the winning full state issaved along with the calculated path metric and the traceback bits inthe decoder state.

As shown in FIG. 10, the bit error rate performance degrades quickly asthe number of super-states is reduced from the full-state value of 32states to 8 super-states. Four states are active per symbol.

The reduced-state maximum likelihood sequence estimator defined inSvennson has only four states. The trellis structure is shown in FIG.11.

As shown in this diagram, a one, two, or three-valued bit causes a statetransition and a zero-valued bit does not. Note that every state isconnected to every other state, which is not shown on the diagram tosimplify the illustration.

Using this method, the inactive states are automatically deleted fromthe path metric computations. This is a simple structure to implementand can be adapted to any CPFSK modulation. As with the set-partitioningapproach, decision feedback is used to maintain the winning phase statefor each of the super states. The decoder then calculates the pathmetrics for the four valid paths from the chosen, winning phase andpicks a new winning path metric, which is then saved in the super statebased on the branch taken during the symbol. If the branch correspondsto a 0-valued bit, then the new super state is the same as the old superstate. If, however, the transition corresponds to a one, two, orthree-valued bit, then the accumulated path metric is saved to thatother super state.

The resulting bit error rate performance is shown in FIG. 12. The BER isslightly degraded by use of the reduced-state technique.

The Continuous Phase Modulation schemes in the MILSTD-188-181C requirecomplex maximum likelihood decoders, which can be reduced in complexityusing either of the two algorithms discussed above. The tilted-phaseapproach has been shown to have the best bit error rate performancewhile proving to be the most computationally efficient. The currentMIL-STD allows for 3 dB implementation loss (for the h= 4/16, 5/16option), which could allow for a receiver to implement the reducedcomplexity scheme and still meet the specification.

There now follows a more detailed description of examples of reducedstate techniques operable with a programmable trellis or maximumlikelihood decoder as described before and used for hybrid CPMmodulation, in accordance with non-limiting examples of the presentinvention.

Hybrid Continuous Phase Modulation (HCPM) is a variant of ContinuousPhase Modulation that uses either additional Amplitude or Phase pulsesto create a higher order modulation. For standard CPM, an increase inthe modulation order results in the increase of the symbol alphabet anda corresponding increase in the transmit bandwidth and exponentialincrease in the complexity of the decoder trellis structure. Hybrid CPMhowever achieves higher order modulation by adding parallel branches tothe base CPM trellis structure thus reducing the receiver complexity.The goal of the text that follows is to demonstrate that the techniquesdevised to reduce the demodulator complexity of standard modulationtypes like TCM and CPM can also be successfully applied to Hybrid CPM.As an example, the text provides an analysis of the power and spectralefficiency of the two hybrid CPM waveforms and gives specific examplesof the application of reduced state techniques. Both set-partitioningand reduced-state sequence estimation with decision feedback techniquesare analyzed and compared. The results will demonstrate thatreduced-state sequence estimation can be coupled with Hybrid CPMdemodulation without any loss in bit error rate performance.

Hybrid Continuous Phase Modulation can be represented with the timedomain representation:

${s(t)} = {\sqrt{2{E/T}}{A_{i}(t)}\cos\;\left( {{2\pi\; f\; t} + {2\pi{\sum\limits_{i = 0}^{n}{\alpha_{i}h_{i}{q_{i}\left( {t - {iT}} \right)}}}}} \right)}$

where T is the symbol period, E is the energy per symbol, f is thecarrier frequency, Ai(t), qi(t), and ai are all dependent on thetransmitted data, and hi is the modulation index. Unlike classic CPMmodulation, hybrid CPM extends the symbol alphabet contained in αi witha set of additional amplitude or phase (Ai(t) or qi(t)) pulses. Forconstant envelope HCPM, qi(t) is the phase pulse shape that containspart of the modulated bits. And for non-constant envelope hybrid CPM,Ai(t) is the amplitude pulse shape that contains part of the modulatedbits. In both cases, the net result is more bits per symbol.

With rectangular (linear) pulse shaping the CPM waveform is denoted as1REC CPM or CPFSK. To this full-response signal, different amplitudepulse shapes can be applied to each CPM phase trajectory to create anon-constant envelope signal. For optimal performance, each amplitudepulse should have good cross-correlation properties and would ideally beorthogonal. A sample set of orthogonal and antipodal signals wouldinclude multiples of sinusoid signals as shown in Table 1.

TABLE I Amplitude Pulse Shaping AM Bit Amplitude Shape 0 A₀₀(t)−sin(Fs/2) 1 A₀₁(t) sin(Fs/2) 2 A₁₀(t) −sin(Fs) 3 A₁₁(t) sin(Fs)

Other CPM-based amplitude pulse schemes have been described in theliterature as a method of reducing the bandwidth of the transmit signal.Multi-amplitude CPM has been defined as a method to increase themodulation order of the CPM signal by allowing same-phase constellationpoints to have two or more amplitude positions. Multi-amplitude CPMreduces the distance between adjacent CPM constellation points and has anarrow transmit spectrum. As a result of the decreased Euclideandistance, the power efficiency of multi-amplitude CPM is impaired by theincrease in constellation density. Unlike multi-amplitude CPMmodulation, hybrid CPM has a the same transmit constellation as theoriginal CPM signal and has a corresponding increase in bandwidth as afunction of each additional bit added to the modulated signal. Ascompared to multi-amplitude CPM, the power efficiency is unaffected byincrease in modulation order. Multi-Amplitude CPM is more comparable toPSK or QAM modulation schemes (and unlike HCPM) because those modulationtypes also increase in constellation density as a function of the orderof the modulation and suffer a corresponding loss in power efficiency.

The constant envelope hybrid CPM modulation utilizes the phase pulse ofthe CPM signal to generate a higher level modulation. Otherconstant-envelope pulse-based modulation schemes have been described inthe literature. Multi-pulse CPM, for example, is a generalized methodthat describes different phase-pulse shapes for each transmitted bitdesigned to provide better Euclidean distance for a given spectral mask.Unlike multi-pulse CPM, the constant envelope hybrid CPM increases themodulation order using both the standard base CPM αi (modulation index)and different phase pulses, qi(t), for the remainder of bits per symbolbeing sent. The resulting signal has the same decoder trellis structureas the base CPM waveform. The additional parallel branches generated bythe HCPM signal are designed in a manner that intentionally prevents anincrease in trellis complexity (only the branch metric computation isaffected).

For constant envelope Hybrid CPM, the phase pulse shape, qi(t), istailored to meet spectral or power efficiency requirements and eachpulse is designed to generate a transmit symbol which is as orthogonalas possible (to other symbols in the transmit alphabet) to increase thedistance properties of the branch metric computation at the decoder. Anexample of the possible phase-pulse shape combinations can best bedemonstrated with a diagram (FIG. 7).

Each possible shape is piece-wise linear for duration of the symbol.This family of phase pulse shapes adds two bits to the CPM modulation.An h=¼ binary CPFSK (1 REC CPM) has a full-state trellis structure asshown in FIG. 8.

The reduced state sequence detection algorithm defines two steps to themodification of the optimal, maximum likelihood decoder such asdescribed above and set forth in the incorporated by reference Svennsonand Eyuboglu articles. The first step is a set-partitioning approach tothe selection of state combination. When the phase constellation isdrawn with the phase positions labeled with each state as shown in FIG.9, showing a h=¼ CPFSK constellation. It becomes apparent that a trellisstructure that creates super states by combining full states 0 and 4, 1and 5, 2 and 6, along with 3 and 7 would provide the best distance forthe reduced state trellis.

This CPM trellis structure already has two special properties. First, ateach symbol, a valid starting state can be either odd or even with theassumption that the first starting state is the zero state. This can beaccomplished at the transmitter by starting the transmission at a phasevalue of zero degrees. Second, the decoder can skip the calculation ofpath metrics for odd or even states at the decoding of every othersymbol. The optimal CPM decoder is already “reduced” to the point thatit only calculates (updates) path metrics for half of the states duringeach decoder cycle.

Referring again to FIG. 1, the reduced-state trellis structure is shown.As noted before, the full state labels are marked in brackets with thenew, super state labels listed above each bracketed pair.

When constructing the reduced state trellis, each full state remainsconnected as it was in the initial trellis. For this specific trellis,the characteristic properties of alternating the start state at eachsymbol decode cycle remains an important parameter of the decoder. Adecode cycle is defined as the calculation of a full state of branchmetrics from an input symbol and the update of the path metrics for allof the active states in the trellis structure.

A second, important enhancement required for reduced state sequencedetection is the decision feedback step in the decoder. Along with pathmetric and trace-back bits, the decoder retains the winning full stateat each super state. Since it is assumed at the beginning that thedecoder starts at super state zero, the decoder state will also assumethat the starting full state is zero and not four. In general, thedecoder super state can be initialized to the first full state in thelist for each of the reduced states (i.e. 0, 1, 2, and 3) byinitializing the path metric properly.

When the decoder calculates the path metric for super state one, it willcompare the zero to one transition (using the corresponding, calculatedbranch metric) to the metric for a state two to state one transition.The decoder saves the full state value of one as the winning state forthe next decoder cycle. The next super state calculated at this decodercycle will be seven (skipping the even, invalid super states). Again,since zero is the winning full state from the initial decoder cycle, thetransition from zero to seven (the only valid full state) to the two tothree (since two was initialized in the previous decoder cycle) and thewinning full state saved along with the calculated path metric and thetrace-back bits in the decoder state.

Hybrid CPM Modulation adds parallel branches to each transition in thetrellis structure. The maximum likelihood decoder must determine, ateach symbol, which parallel branch has the best distance (the bestnumerical branch metric value) and uses that value for the currentstate-to-state transition. Standard CPM complexity increases with themodulation level and h-value. Hybrid CPM does not add states ortransition branches to the trellis structure. The complexity of theHybrid CPM modulation has a proportional increase based on the number ofbranch metrics required for each bit added to the modulation level.

Another characteristic feature of hybrid CPM is the ability to tailorthe transmit spectrum to meet channel requirements. As shown in theexample in Table 1 above, a single bit can be added to the CPFSKmodulation using a ½ sine wave amplitude shape. If two bits are added, afull sine wave amplitude pulse is added to the existing sine wave toform four antipodal pulse shapes. The resulting spectra are shown inFIG. 13.

Each spectrum has been normalized to the bit rate rather than the symbolrate to demonstrate that the characteristic bandwidth of the CPFSKsignal has been preserved. In fact, the bandwidth is increased by thenumber of bits per symbol in the Hybrid CPM waveform. The resulting 90%bandwidth values are 0.68, 2.1, and 3.4 times the symbol rate for theCPFSK, Hybrid CPM with 1 AM Bit, and Hybrid CPM with 2 AM Bitsrespectively.

The amplitude pulse shaped Hybrid CPM has the spectral properties asshown in FIG. 14. As with the phase pulse shaping, the amplitude pulseshapes add spectral content to the signal. Each spectrum shown in FIG.11 has been normalized to the bit rate of the modulation. Withoutnormalization, the resulting 90% bandwidth is 0.68, 1.5, and 3.4 timesthe symbol rate.

An intuitive expectation of a waveform that increases bandwidth as afunction of modulation level is that the distance property of the signalmust be increasing and the corresponding power efficiency is improved.This is equivalent to a PSK signal that has been spread by an orthogonalcode. The resulting signal bandwidth increases by the code rate and thepower efficiency is the same as a standard PSK modulation. In the caseof pulse shapes chosen as examples, some provide more or less bandwidthexpansion and correspondingly more or less Eb/No improvement. As shownin FIG. 15, the amplitude pulse shaped Hybrid CPM has differentperformance levels for each pulse shape.

The abbreviation “IRS” is used to represent the reduced state version ofeach of the Hybrid CPM examples. As shown in FIG. 15, the higherthroughput, 3 bits per symbol, Hybrid CPM modulation, has better powerefficiency than the 2 bits per symbol version. It has been verified thatby selecting the wider bandwidth, i.e., full sine wave amplitude pulseshapes, the Eb/No performance was improved for the 2 bit per symbolHybrid CPM.

The power efficiency of the 3 bit per symbol Hybrid CPM signal matchesthe standard h=¼ CPFSK modulation. Those skilled in the art understandthat it is possible to increase the modulation level of the CPFSKsignal. The decoder complexity can increase with the modulation level.The number of states in the CPM trellis can be the same for themulti-level as for the binary modulation, but each state has anincreasing number of branches as the order of the modulation increases.The decoder calculates the metric for each of these transition branchesas the sum of the branch metric and the path metric of its associatedstate. If the transition branch is not chosen, this is a wastedoperation. In the case of the parallel branches used by Hybrid CPM, thedecoder simply compares branch metrics of the two parallel paths withoutthe addition of the path metric. Depending on the number of states andmodulation order, the extra addition of the path metric increases therelative complexity of the standard CPM modulation relative to theHybrid CPM modulation.

The phase pulse shaped Hybrid CPM modulation bit error rate curves areshown in FIG. 16. As with the amplitude pulse shaping, the phase pulseshaping performance is variable. The 3 bit per symbol modulationoutperforms the 2 bit per symbol version. Again, the difference is inthe choice of phase pulse shapes. If the higher-valued pulse shaping waschosen for the 2 bit per symbol Hybrid CPM, the power efficiency wouldbe improved.

The resulting bit error rate curve for the 2-state reduced state h=⅓CPFSK and HCPM with amplitude shaping is shown in FIG. 17.

The bit error rate curve for the 2-state reduced state h=⅓ CPFSK withHCPM with phase pulse shaping is shown in FIG. 18.

For increased modulation order (4-ary, 8-ary, etc.). The reduced statetrellis structure increases proportionally. For HCPM, however, thetrellis structure of the original CPM signal is maintained. The trellisstructure has parallel branches, which do not modify the decisionfeedback or path metric storage. The best parallel path is chosen foreach branch and then used as the branch metric for that super state.

It is clear from the power efficiency performance curves that thepairing of reduced-state sequence detection with Hybrid CPM modulationeffectively extends the range of usefulness of the waveform. Increasingthe throughput of a CPM signal with the addition of the orthogonalamplitude or phase modulation does not increase the decoder complexityas much as adding more transition branches to each node. With theaddition of reduced state sequence detection, additional powerefficiency performance can be obtained without the correspondingincrease in decoder complexity through the use of a base CPM trellisstructure with a larger number of full states.

Each possible pulse shape is piece-wise linear for the duration of thesymbol. This family of phase pulse shapes adds 2 bits to the CPMmodulation.

As an illustration of both types of hybrid CPM modulation, a common basetrellis structure was selected. An h=¼ binary CPFSK (LREC CPM) has afull-state trellis structure with eight states as shown in FIG. 5showing a h=¼ CPFSK trellis.

This application is related to copending patent applications entitled,“REDUCED STATE TRELLIS DECODER USING PROGRAMMABLE TRELLIS PARAMETERS,”which is filed on the same date and by the same assignee and inventors,the disclosure which is hereby incorporated by reference.

Many modifications and other embodiments of the invention will come tothe mind of one skilled in the art having the benefit of the teachingspresented in the foregoing descriptions and the associated drawings.Therefore, it is understood that the invention is not to be limited tothe specific embodiments disclosed, and that modifications andembodiments are intended to be included within the scope of the appendedclaims.

1. A decoder comprising: at least one programming input for a pluralityof programmable reduced-state trellis parameters; and a programmabledevice connected to the at least one programming input and implementinga reduced-state maximum likelihood decoder comprising at least onereduced-state trellis structure based upon the plurality of programmablereduced-state trellis parameters and that is operable for processing acontinuous phase modulated (CPM) signal and returning up to N bits thatwere transmitted based on a maximum likelihood and current winningsuper-state and corresponding survivor full-state, wherein saidprogrammable device calculates the path metrics for every super-stateand determines a best path based on the programmable reduced-statetrellis parameters.
 2. The decoder according to claim 1, wherein saidprogrammable reduced-state trellis parameters are comprised of one of atleast the number of super-states, the number of full-states, the numberof branches per super-state, a reverse super-state trellis table, adecoder super-state survivor as a full-state, a forward full-statetable, a full-state to super-state mapping table, decoder super-statepath metric and decoder super-state traceback array.
 3. The decoderaccording to claim 2, wherein all programmable parameters are integers.4. The decoder according to claim 2, wherein the decoder state structurecomprises a path metric per super-state, a traceback array persuper-state, and a survivor full-state per super-state.
 5. Theprogrammable decoder according to claim 2, wherein the reduced-statetrellis structure is formed from an Ungerboeck-Style set-partitioningalgorithm.
 6. The programmable decoder according to claim 2, wherein thereduced-state trellis structure is formed from a two-stateSvensson-Style structure.
 7. The programmable decoder according to claim2, wherein the reduced-state trellis structure is formed from a M-stateSvensson-style structure.
 8. The programmable decoder according to claim1, wherein the reduced-state maximum likelihood decoder furthercomprises a decoder state structure that contains path metrics and afull decoder state used for decision feedback.
 9. The programmabledecoder according to claim 1, wherein the reduced-state maximumlikelihood decoder further comprises a Forward Trellis structureoperative for indicating which full decoder state from a decisionfeedback is connected to a next full decoder state for any given symbol.10. The programmable decoder according to claim 1, and furthercomprising at least one output connected to said programmable device foroutputting decoded bits with multiple bits per output.
 11. Theprogrammable decoder according to claim 8, wherein the at least oneoutput is operative for outputting a full traceback of decoded bits fora best path.
 12. A decoder comprising: at least one programming inputfor a plurality of programmable reduced-state trellis parameters; and aprogrammable device connected to the at least one programming input andimplementing a reduced-state maximum likelihood decoder comprising atleast one reduced-state trellis structure based upon the plurality ofprogrammable reduced-state trellis parameters and that is operable forprocessing a continuous-phase modulated (CPM) signal and returning Nbits that were transmitted based on a maximum likelihood and currentwinning super-state and corresponding survivor full-state, wherein saidprogrammable device calculates the path metrics for every super stateand determines a best path based on a forward state trellis when awinning full-state is received and full-states are combined into asuper-state based on the programmable reduced-state trellis parameters.13. The decoder according to claim 12, wherein said programmablereduced-state trellis parameters comprise one of at least the number ofsuper-states, the number of full-states, the number of branches persuper-state, a reverse super-state trellis table, a decoder super-statesurvivor as a full-state, a forward full-state table, a full-state tosuper-state mapping table, decoder super-state path metric and decodersuper-state traceback array.
 14. The decoder according to claim 13,wherein the number of super states, full states and branches per nodecomprise an integer.
 15. The decoder according to claim 13, wherein thedecoder state structure comprises path metrics, full decoder state usedfor decision feedback and traceback array.
 16. The programmable decoderaccording to claim 12, wherein the reduced-state maximum likelihooddecoder comprises a Forward full-state Trellis structure operative forindicating which full decoder state from a decision feedback isconnected to a next full decoder state for any given symbol.
 17. Theprogrammable decoder according to claim 12, and further comprising atleast one output connected to said programmable device for outputtingdecoded bits with multiple bits per output.
 18. The programmable decoderaccording to claim 17, wherein the at least one output is operative foroutputting a full traceback of all decoded bits for the current bestpath metric.
 19. A method of implementing a decoder comprising:inputting a plurality of programmable reduced-state trellis parameters;and implementing within a programming device a reduced-state maximumlikelihood decoder comprising at least one reduced state trellisstructure based upon the plurality of programmable trellis parametersand processing a continuous phase modulated (CPM) signal and returning Nbits that were transmitted based on a maximum likelihood and currentwinning reduced-state, calculating the path metrics for everysuper-state and determining a best path based on the programmablereduced-state trellis parameters.
 20. The method according to claim 19,which further comprises demodulating within the programming devicewaveforms with memory.
 21. The method according to claim 19, whichfurther comprises forming a decoder state structure which contains pathmetrics, a surviving full-state used for decision feedback and atraceback array.
 22. The method according to claim 19, which furthercomprises forming a Forward Trellis structure operative for indicatingwhich surviving full decoder state from a decision feedback is connectedto a next full decoder state for any given symbol.
 23. The programmabledecoder according to claim 19, wherein the reduced-state trellisstructure is formed from an Ungerboeck-Style set-partitioning algorithm.24. The programmable decoder according to claim 19, wherein thereduced-state trellis structure is formed from a two-stateSvensson-Style structure.
 25. The programmable decoder according toclaim 19, wherein the reduced-state trellis structure is formed from aM-state Svensson-style structure.
 26. A decoder comprising: at least oneprogramming input for a plurality of programmable reduced-state trellisparameters; and a programmable device connected to the at least oneprogramming input and implementing a reduced-state maximum likelihooddecoder that is operable for processing a continuous phase modulated(CPM) signal and returning up to N bits that were transmitted based on amaximum likelihood and current winning super-state and correspondingsurvivor full-state, wherein said programmable device calculates thepath metrics for every super-state and determines a best path based onthe reduced-state trellis parameters, wherein said programmablereduced-state trellis parameters are comprised of one of at least thenumber of super-states, the number of full-states, the number ofbranches per super-state, a reverse super-state trellis table, a decodersuper-state survivor as a full-state, a forward full-state table, afull-state to super-state mapping table, decoder super-state path metricand decoder super-state traceback array.
 27. A decoder comprising: atleast one programming input for a plurality of programmablereduced-state trellis parameters; and a programmable device connected tothe at least one programming input and implementing a reduced-statemaximum likelihood decoder that is operable for processing acontinuous-phase modulated (CPM) signal and returning N bits that weretransmitted based on a maximum likelihood and current winningsuper-state and corresponding survivor full-state, wherein saidprogrammable device calculates the path metrics for every super stateand determines a best path based on a forward state trellis when awinning full-state is received and full-states are combined into asuper-state based on the reduced-state trellis parameters, wherein saidprogrammable reduced-state trellis parameters comprise one of at leastthe number of super-states, the number of full-states, the number ofbranches per super-state, a reverse super-state trellis table, a decodersuper-state survivor as a full-state, a forward full-state table, afull-state to super-state mapping table, decoder super-state path metricand decoder super-state traceback array.
 28. A method of implementing adecoder comprising: inputting a plurality of programmable reduced-statetrellis parameters; processing within a programming device a continuousphase modulated (CPM) signal and returning N bits that were transmittedbased on a maximum likelihood and current winning reduced-state,calculating the path metrics for every super-state and determining abest path based on the reduced-state trellis parameters; and forming aForward Trellis structure operative for indicating which surviving fulldecoder state from a decision feedback is connected to a next fulldecoder state for any given symbol.